>>2757183The bike's frame design and materials affect how it rides - more comfort/upright, relaxed & stable, stretched out with faster steering, etc. "Geometry" means things like the wheelbase, seat & head tube angles, chainstay length, fork rake - if that sounds like jargon you don't care about, try riding a road bike, mountain bike, and a touring bike vs your city bike. You'll get it.
For longer trips you're looking for a touring bike or one of the non-racing cyclocross "adventure" or "gravel" bike like the other poster said. You want lots of gears, rack mounts, decent wheels, and preferably durable but not heavy construction like your city bike.
there are /n/ folks who bikepack, worth a lurk